在刚刚落下帷幕的2006年高考中,湖北省一些重点中学的理科考生仍对其中的二三道试题叫苦叫难,这里面就包括第15题:将杨辉三角形中的每一个数Crn都换成分图1数1(n+1)Crn,就得到一个如图1所示的分数三角形,称为莱布尼茨三角形.从莱布尼茨三角形可看出1(n+1)Crn+1(n+1)Cxn=1nCnr-1 In the 2006 college entrance examination that had just ended, the science candidates in some key middle schools in Hubei province still complained about the second and third test questions. This includes the 15th question: Replace each number Crn in the triangle of Yang Hui Dividing the number 1 (n+1)Crn in the subgraph 1 yields a fractional triangle as shown in Fig. 1, which is called the Leibniz triangle. From the Leibniz triangle, we can see that 1(n+1)Crn+1. (n+1)Cxn=1nCnr-1